TY - GEN
T1 - Auctions with online supply
AU - Babaioff, Moshe
AU - Blumrosen, Liad
AU - Roth, Aaron
PY - 2010
Y1 - 2010
N2 - We study the problem of selling identical items to n unit-demand bidders in a setting in which the total supply of items is unknown to the mechanism. Items arrive dynamically, and the seller must make the allocation and payment decisions online with the goal of maximizing social welfare. We consider two models of unknown supply: the adversarial supply model, in which the mechanism must produce a welfare guarantee for any arbitrary supply, and the stochastic supply model, in which supply is drawn from a distribution known to the mechanism, and the mechanism need only provide a welfare guarantee in expectation. Our main result is a separation between these two models. We show that all truthful mechanisms, even randomized, achieve a diminishing fraction of the optimal social welfare (namely, no better than a Ω(log log n) approximation) in the adversarial setting. In sharp contrast, in the stochastic model, under a standard monotone hazard-rate condition, we present a truthful mechanism that achieves a constant approximation. We show without any condition on the supply distribution, no mechanism can achieve a constant fraction approximation. We also characterize a natural subclass of truthful mechanisms in our setting, the set of online-envy-free mechanisms. All of the mechanisms we present fall into this class, and we prove almost optimal lower bounds for such mechanisms. Since auctions with unknown supply are regularly run in many online-advertising settings, our main results emphasize the importance of considering distributional information in the design of auctions in such environments.
AB - We study the problem of selling identical items to n unit-demand bidders in a setting in which the total supply of items is unknown to the mechanism. Items arrive dynamically, and the seller must make the allocation and payment decisions online with the goal of maximizing social welfare. We consider two models of unknown supply: the adversarial supply model, in which the mechanism must produce a welfare guarantee for any arbitrary supply, and the stochastic supply model, in which supply is drawn from a distribution known to the mechanism, and the mechanism need only provide a welfare guarantee in expectation. Our main result is a separation between these two models. We show that all truthful mechanisms, even randomized, achieve a diminishing fraction of the optimal social welfare (namely, no better than a Ω(log log n) approximation) in the adversarial setting. In sharp contrast, in the stochastic model, under a standard monotone hazard-rate condition, we present a truthful mechanism that achieves a constant approximation. We show without any condition on the supply distribution, no mechanism can achieve a constant fraction approximation. We also characterize a natural subclass of truthful mechanisms in our setting, the set of online-envy-free mechanisms. All of the mechanisms we present fall into this class, and we prove almost optimal lower bounds for such mechanisms. Since auctions with unknown supply are regularly run in many online-advertising settings, our main results emphasize the importance of considering distributional information in the design of auctions in such environments.
KW - approximation
KW - mechanism design
KW - online supply
KW - truthful auction
UR - http://www.scopus.com/inward/record.url?scp=77954721425&partnerID=8YFLogxK
U2 - 10.1145/1807342.1807345
DO - 10.1145/1807342.1807345
M3 - Conference contribution
AN - SCOPUS:77954721425
SN - 9781605588223
T3 - Proceedings of the ACM Conference on Electronic Commerce
SP - 13
EP - 22
BT - EC'10 - Proceedings of the 2010 ACM Conference on Electronic Commerce
T2 - 11th ACM Conference on Electronic Commerce, EC'10
Y2 - 7 June 2010 through 11 June 2010
ER -